in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example.

In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.

‎In this paper‎, ‎we formulate the sixth-order boundary value problem as Fredholm integral equation by finding Green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎Also nonexistence results are obtained‎. ‎An example is given to illustrate the results of paper‎.

‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

In this paper‎, ‎first we propose a new method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equations of the second kind based on the fuzzy wavelet like operator‎. ‎Then‎, ‎we discuss and investigate the convergence and error analysis of the proposed method‎. ‎Finally‎, ‎to show the accuracy of the proposed method‎, ‎we present two numerical ‎examples.‎

In this paper, He‘s variational iteration method is applied to Fredholm integral equations of the second kind. To illustrate the ability and simplicity of the method, some examples are provided. The results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

 Abstract: In this paper homotopy perturbation is applied to system of linear Fredholm integral equations of the first kind .For these systems, degenerate kernels are considered and in order to avoid successive integrations ,an easy matrix computation is derived for approximating the solution of the problem.  

‎In this paper‎, ‎we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered‎ ‎extended partial $b$-metric space‎. ‎We also develop an‎ ‎application for Fredholm type integral equations to‎ ‎validate our main result and a non-trivial example is given to‎ ‎elucidate our work.

We apply the Kurzweil-Henstock integral setting to prove a Fredholm Alternative-type result for the integral equation x (t)− K Z [a,b] α (t, s)x (s) ds = f (t) , t ∈ [a, b] , where x and f are Kurzweil integrable functions (possibly highly oscillating) defined on a compact interval [a, b] of the real line with values on Banach spaces. An application is given.